109edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
109edo [[tempering out|tempers out]] 20000/19683 ([[tetracot comma]]) in the [[5-limit]]; [[245/243]], [[2401/2400]] and [[65625/65536]] in the [[7-limit]]; [[385/384]], [[1375/1372]], and [[4000/3993]] in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11- and 13-limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot. | 109edo [[tempering out|tempers out]] 20000/19683 ([[tetracot comma]]) in the [[5-limit]]; [[245/243]], [[2401/2400]] and [[65625/65536]] in the [[7-limit]]; [[385/384]], [[1375/1372]], and [[4000/3993]] in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11- and 13-limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot. | ||
109edo has an excellent [[7/1|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/ | 109edo has an excellent [[7/1|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/2254, 2300/2299, 6860/6859, 10241/10240. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|109}} | {{Harmonics in equal|109|columns=16}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
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== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=v_J71U392_k '' | * "Teenagerges" from ''TOTMC September to December 2024'' (2024) – [https://open.spotify.com/track/4oQglJSEyp6CsL5RNWuiBy Spotify] | [https://francium223.bandcamp.com/track/teenagerges Bandcamp] | [https://www.youtube.com/watch?v=v_J71U392_k YouTube] – in Tetracot[13], 109edo tuning | ||
* "Catbabel" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/0T7nW3ziEFvjV8c7v1EaMB Spotify] | [https://francium223.bandcamp.com/track/catbabel Bandcamp] | [https://www.youtube.com/watch?v=gtnTdPqiTDQ YouTube] | |||
== See also == | == See also == | ||
* [[109-7-comma]] | * [[109-7-comma]] | ||